Accomplishments and achievements doesn’t really determine how good s teacher is.
Yeah, but you can't rely on your childs enjoyment either. I've had MANY transfer students who loved their last teacher - they were probably funny, nice etc... but they completely hampered their ability to progress steadily, making the student do an obscene amount of work that barely extends their skills. I've known students who have been playing for years and can barely read the notes... but they enjoyed being taught by their last teacher.
I can't stress enough how much I identify with these words as it has been my own experience too.